That consensus, Deutsche Bank says, is driving growing strength
in the markets.

Here is what Di Lizia has to say (emphasis ours):

The upcoming EU referendum continues to represent a significant
driver of risk dynamics. However, with the referendum now less
than 5 weeks away the market has shown signs of
increasingly pricing out the likelihood of a Brexit across a
range of financial market variables. Over the past week,
a shift in the latest opinion polls towards a stronger lead for
remain together with bookmaker’s implied probabilities
underlining a clear lead for “Bremain” has helped drive
more hawkish front end pricing, a tightening in basis markets and
an appreciation in sterling.

From next Friday (27th May) the pre-referendum “purdah” period
begins which will restrict the ability for those connected to
government to campaign for either outcome. As a result,
some of the noise surrounding the current campaign should be
expected to die down, which may help the market
consolidate around current probabilities as we approach the 23rd
June. However, given the speed of this upward revision in the
market’s probability of a “Bremain,” the risk remains for some
retracement in the polls, which would become increasingly
significantly as the vote gets closer.

Here are the charts Deutsche argues have helped the market start
to price out Brexit:

Deutsche
Bank

Deutsche
Bank

Deutsche Bank pointed to increased expectations going forward
across a variety of asset classes, including the pound, sovereign
credit, and equities:

Ultimately, the signal to noise ratio from these polls remains
poor while a wide spread exists between telephone and online
polls. Nevertheless, these recent moves have led the market to
revise lower the expected Brexit probability across a range of
variables, repricing expectations of easing at the UK front end,
strengthening sterling and driving UK basis and sovereign CDS
spreads to retrace from their wides.

This isn't the first time that a seemingly decreased likelihood
of Brexit has helped drive strength in the UK's markets.
Earlier in May, Business Insider reported that currency
traders in the UK were getting less and less worried about Brexit
actually occurring, which helped the pound rebound strongly from
multi-year lows early in 2016.

Deutsche Bank added that the recent strengthening in the
pound, which has seen it gain more than 5% since the lows seen in
February, has been strongly tied to Brexit polling — if polls
favour remain, then sterling will move higher, and vice versa.